Limacon
r = a+b sin theta
r = a+b cos theta
Cardioid
a-b sin theta
a-b cos theta
Rose
r = a sin n theta
r = a cos n theta
n is how many petals
Archimedes Spiral
r = a theta +b
Logarithmic Spiral
r=a^theta b
Converting
polar to rectangular
x=r cos theta
y=r sin theta
rectangular to polar
r=+/- sqrt x^2 + y^2
theta is (x/y)
Trig Chart:
0°
sin0=0
cos0=1
tan0=undefined
sec0=1
cot0=0
30°
sinπ/6=1/2
cosπ/6=√3/2
tanπ/6=√3/3
cscπ/6=2
secπ/6=2 √3/3
cotπ/6=√3
45°
sinπ/4=√2/2
cosπ/4=√2/2
tanπ/4=1
cscπ/4=√2
secπ/4=√2
cotπ/4=1
60°
sinπ/3=√3/2
cosπ/3=1/2
tanπ/3=√3
cscπ/3=2 √3/3
secπ/3=2
cotπ/3=√3/2
90°
sinπ/2=1
cosπ/2=0
tanπ/2=undefined
cscπ/2=1
secπ/2=undefined
cotπ/2=0
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For example:
ReplyDeletex² + 6x - 2 = 0
* anytime you are solving a quadratic you’re finding x-intercepts
Move the constant term to the right side:
x² + 6x = 2
Take half of the coefficient on the x-term (divide it by two, and keeping the sign), and then square it. Add the squared value to both sides of the equation:
x² + 6x + 9 = -2 + 9
Convert the left-hand side to squared form. Simplify the right-hand side:
(x + 3)² = 7
* the # half of the coefficient goes in the parentheses.
Square-root both sides:
x + 3 = √7
Solve for "x =". Remember to put the "±" on the right side and that it gives you two solutions.
x = -3 ± √7
The two points for this solution are:
(-3 + √7) , (-3 -√7)